equation_sheet

# Sphere shell radius r diameter 23 mr 2 rod length l

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sphere shell, radius R diameter 2/3 mR 2 rod, length L end 1/3 mL 2 sphere, radius R tangent 7/5 mR 2 rect. sheet, length L central 1/12 mL 2 rect. sheet, length L edge 1/3 mL 2 V V B A F h x S A F l l Y A F P I I W I K I I L p r L dt L d F r F r k b a b a j b a b a i b a b a b a c i f z x y y x z x x z y z z y Δ = Δ = Δ = = - = = = = × = = × = = - + - + - = × = ω τ ω ω ω α τ ω τ τ φ τ 2 2 1 2 2 1 rot 2 2 1 net sin ˆ ) ( ˆ ) ( ˆ ) ( arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp arrowrightnosp ( ) 2 3 2 2 2 2 2 1 2 2 4 c GM R R GM v a GM T r GmM U h r GM g r m m G F S esc g = = = - = + = = π ( ) v A P T v f v k t kx A t y 2 2 2 1 2 sin ) ( μω μ λ λ π ω = = = = - = constant constant 2 2 1 disp fluid 0 = + + = = + = = gy v P Av gV B gh P P A F P ρ ρ ρ ρ ρ ( ) ( ) 2 2 2 0 2 0 2 2 2 cos ) ( + - = - = = = = = + = m b m F A m b m k T I mgd L g m k t A t x ω ω ω ω π ω ω ω ω φ ω S S O C v v f v v v v f I I s v k s v P s v A Power I T B v = ± = = = = Δ = = + = = θ β ω ρ ρ ω ρ ρ sin ' log 10 273 1 331 0 max max 2 max 2 max 2 2 1 2 1 , 5 , 3 , 1 , 4 4 , 3 , 2 , 1 , 2 2 f f f n L v n f n L n L v n f n L beat n n n n - = = = = = = = λ λ T Nk

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